Is there a way to export an object without all of it's inside geometry?
I want to say the answer is no - for what you're describing. 

Maybe there's a script out there that does it for you but it sounds like something you might have to write up yourself. ?

In my experience, I would typically hand-delete them, separate them.

It also sounds like a lot of work to fix and might need to look into another workflow method...

Good luck!